English

The Length of the Perpendicular Drawn from the Point P(A, B, C) from Z-axis is

Advertisements
Advertisements

Question

The length of the perpendicular drawn from the point P(a, b, c) from z-axis is 

Options

  • \[\sqrt{a^2 + b^2}\] 

  • \[\sqrt{b^2 + c^2}\] 

  • \[\sqrt{a^2 + c^2}\]

  •  \[\sqrt{a^2 + b^2 + c^2}\]

MCQ
Advertisements

Solution

The length of the perpendicular drawn from the point P(x, y, z) from z-axis is given by \[\sqrt{y^2 + x^2}\] Thus, the length of the perpendicular drawn from the point P(a, b, c) from z-axis is \[\sqrt{a^2 + b^2}\] 

Hence, the correct answer is option (a)

shaalaa.com
  Is there an error in this question or solution?
Chapter 28: Introduction to three dimensional coordinate geometry - Exercise 28.5 [Page 23]

APPEARS IN

R.D. Sharma Mathematics [English] Class 11
Chapter 28 Introduction to three dimensional coordinate geometry
Exercise 28.5 | Q 15 | Page 23

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

Name the octants in which the following points lie: (5, 2, 3)


Name the octants in which the following points lie:

(–5, 4, 3) 


Name the octants in which the following points lie: 

 (7, 4, –3)


Name the octants in which the following points lie: 

(–5, –4, 7) 


Name the octants in which the following points lie: 

(–7, 2 – 5)


Find the image  of: 

 (–2, 3, 4) in the yz-plane.


Find the image  of: 

 (–5, 4, –3) in the xz-plane. 


Find the image  of: 

 (–4, 0, 0) in the xy-plane. 


Find the distances of the point P(–4, 3, 5) from the coordinate axes. 


Verify the following: 

 (–1, 2, 1), (1, –2, 5), (4, –7, 8) and (2, –3, 4) are vertices of a parallelogram.


Verify the following:

 (5, –1, 1), (7, –4,7), (1, –6,10) and (–1, – 3,4) are the vertices of a rhombus.


Find the equation of the set of the points P such that its distances from the points A(3, 4, –5) and B(–2, 1, 4) are equal.


Find the ratio in which the line segment joining the points (2, 4,5) and (3, −5, 4) is divided by the yz-plane.


The coordinates of the foot of the perpendicular drawn from the point P(3, 4, 5) on the yz- plane are


The perpendicular distance of the point P (6, 7, 8) from xy - plane is


The length of the perpendicular drawn from the point P (3, 4, 5) on y-axis is 


If the direction ratios of a line are 1, 1, 2, find the direction cosines of the line.


Find the direction cosines of the line passing through the points P(2, 3, 5) and Q(–1, 2, 4).


A line makes equal angles with co-ordinate axis. Direction cosines of this line are ______.


If a line makes angles `pi/2, 3/4 pi` and `pi/4` with x, y, z axis, respectively, then its direction cosines are ______.


Find the equation of the plane through the points (2, 1, 0), (3, –2, –2) and (3, 1, 7).


Find the equations of the two lines through the origin which intersect the line `(x - 3)/2 = (y - 3)/1 = z/1` at angles of `pi/3` each.


O is the origin and A is (a, b, c). Find the direction cosines of the line OA and the equation of plane through A at right angle to OA.


Find the length and the foot of perpendicular from the point `(1, 3/2, 2)` to the plane 2x – 2y + 4z + 5 = 0.


Show that the points `(hati - hatj + 3hatk)` and `3(hati + hatj + hatk)` are equidistant from the plane `vecr * (5hati + 2hatj - 7hatk) + 9` = 0 and lies on opposite side of it.


If l1, m1, n1 ; l2, m2, n2 ; l3, m3, n3 are the direction cosines of three mutually perpendicular lines, prove that the line whose direction cosines are proportional to l1 + l2 + l3, m1 + m2 + m3, n1 + n2 + n3 makes equal angles with them.


The area of the quadrilateral ABCD, where A(0, 4, 1), B(2,  3, –1), C(4, 5, 0) and D(2, 6, 2), is equal to ______.


The locus represented by xy + yz = 0 is ______.


The vector equation of the line `(x - 5)/3 = (y + 4)/7 = (z - 6)/2` is ______.


The unit vector normal to the plane x + 2y +3z – 6 = 0 is `1/sqrt(14)hati + 2/sqrt(14)hatj + 3/sqrt(14)hatk`.


The line `vecr = 2hati - 3hatj - hatk + lambda(hati - hatj + 2hatk)` lies in the plane `vecr.(3hati + hatj - hatk) + 2` = 0.


The vector equation of the line `(x - 5)/3 = (y + 4)/7 = (z - 6)/2` is `vecr = (5hati - 4hatj + 6hatk) + lambda(3hati + 7hatj - 2hatk)`.


If the foot of perpendicular drawn from the origin to a plane is (5, – 3, – 2), then the equation of plane is `vecr.(5hati - 3hatj - 2hatk)` = 38.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×